Step-by-step explanation:
Let V be the volume of the cone.
The student says that, the volume of a cone with a 4-inch diameter is two times the volume of a cone with the same height and a 2-inch radius.
If diameter is 4 inch, radius = 2 inch
Volume of the cone,
[tex]V=\dfrac{\pi }{3}\times 2^2\times h\\\\V=\dfrac{4\pi h}{3}[/tex] .......(1)
If radius, r = 2 inch
New volume,
[tex]V=\dfrac{\pi }{3}\times 2^2\times h\\\\V=\dfrac{4\pi h}{3}[/tex] ....(2)
We can see that the volume in both case is same. Hence, the student is correct.
